The study of the structure and function of proteins raises many problems that offer challenges and opportunities for computational and statistical research. I will overview my experiences in several such problem domains, ranging from domains where off-the-shelf ideas can be fruitfully applied to domains that require new thinking. These are: (1) the identification of active sites in enzymes;(2) the modeling of protein backbone configurations; (3) the prediction of molecular function based on phylogeny; (4) joint inference of alignment and phylogeny.